Cylindrical shells under combined loading

A main feature of this yield behaviour of metal components in a multi-axial stress state is that stress components with the same sign (e.g. biaxial compression) support each other, while stresses with different signs or additional shear stresses lower the yield carrying capacity in each direction. A set of calculations investigating the interaction of axial compression and external pressure is reported by Galletly and Pemsing (1985). The fy -related curves calculated therein at different levels of yield strength show essential differences, even more with respect to elastic buckling. To clarify the GMNA behaviour, further calculations have been performed at the University of Essen using an ideal bilinear elasticplastic material law (Winterstetter 2000). They are included in Figs 10.7 and 10.8. In general, GMNA calculations yield buckling interaction curves which approach asymptotically either the elastic GNA interaction curve (where elastic buckling occurs below the yield limit) or the yield limit curve (where the elastic buckling stress state is beyond the yield limit). The GMNA curves of thickwalled shells follow completely the shape of the yield limit curve, thus including load-reducing effects of the elasticplastic material subject to a biaxial stress state. Geometrically and materially nonlinear analysis, imperfect geometry (GMNIA) The main cause for the severe discrepancies between the theoretical axial compression buckling load of a perfect thin cylindrical shell and the experimetal results has long been shown by many authors to be the geometrical imperfections. Thus, if one wants to calculate the ultimate load carrying capacity of a cylinder directly and with the highest-possible accuracy, an imperfect model has to be employed. Many works have been done on calculating the loaddeection path and buckling strength of imperfect cylindrical shells under the fundamental loads (e.g. Hutchinson 1965; Booton and Tennyson 1979; Galletly and Pemsing 1985; Rotter 1997). Though, only a few reports exist that deal with interactive buckling, and if so, only a small range of possible dimensions and load ratios is covered. From a structural engineers point of view, the buckling strength of a particular shell which is to be designed is of interest. The actual imperfections are of course unknown at the design stage, so they have to be replaced by so-called substitute equivalent geometric imperfections. For a design by global numerical GMNIA, one has to assume a proper equivalent geometric imperfection pattern and a sufcient amplitude for the design to be safe. Some recently issued shell buckling design codes (DASt 1992; CEN 1998) give recommendations on which patterns and amplitudes should be used. As a guide, one possible unfavourable pattern is the critical buckling mode (eigenvector of